Kristofer Bouchard

Rui Meng, Tianyi Luo, Kristofer Bouchard

Unsupervised learning plays an important role in many fields, such as artificial intelligence, machine learning, and neuroscience. Compared to static data, methods for extracting low-dimensional structure for dynamic data are lagging. We developed a novel information-theoretic framework, Compressed Predictive Information Coding (CPIC), to extract useful representations from dynamic data. CPIC selectively projects the past (input) into a linear subspace that is predictive about the compressed data projected from the future (output). The key insight of our framework is to learn representations by minimizing the compression complexity and maximizing the predictive information in latent space. We derive variational bounds of the CPIC loss which induces the latent space to capture information that is maximally predictive. Our variational bounds are tractable by leveraging bounds of mutual information. We find that introducing stochasticity in the encoder robustly contributes to better representation. Furthermore, variational approaches perform better in mutual information estimation compared with estimates under a Gaussian assumption. We demonstrate that CPIC is able to recover the latent space of noisy dynamical systems with low signal-to-noise ratios, and extracts features predictive of exogenous variables in neuroscience data.

Luca Pion-Tonachini, Kristofer Bouchard, Hector Garcia Martin et al.

We outline emerging opportunities and challenges to enhance the utility of AI for scientific discovery. The distinct goals of AI for industry versus the goals of AI for science create tension between identifying patterns in data versus discovering patterns in the world from data. If we address the fundamental challenges associated with "bridging the gap" between domain-driven scientific models and data-driven AI learning machines, then we expect that these AI models can transform hypothesis generation, scientific discovery, and the scientific process itself.

Rui Meng, Kristofer Bouchard

Many modern time-series datasets contain large numbers of output response variables sampled for prolonged periods of time. For example, in neuroscience, the activities of 100s-1000's of neurons are recorded during behaviors and in response to sensory stimuli. Multi-output Gaussian process models leverage the nonparametric nature of Gaussian processes to capture structure across multiple outputs. However, this class of models typically assumes that the correlations between the output response variables are invariant in the input space. Stochastic linear mixing models (SLMM) assume the mixture coefficients depend on input, making them more flexible and effective to capture complex output dependence. However, currently, the inference for SLMMs is intractable for large datasets, making them inapplicable to several modern time-series problems. In this paper, we propose a new regression framework, the orthogonal stochastic linear mixing model (OSLMM) that introduces an orthogonal constraint amongst the mixing coefficients. This constraint reduces the computational burden of inference while retaining the capability to handle complex output dependence. We provide Markov chain Monte Carlo inference procedures for both SLMM and OSLMM and demonstrate superior model scalability and reduced prediction error of OSLMM compared with state-of-the-art methods on several real-world applications. In neurophysiology recordings, we use the inferred latent functions for compact visualization of population responses to auditory stimuli, and demonstrate superior results compared to a competing method (GPFA). Together, these results demonstrate that OSLMM will be useful for the analysis of diverse, large-scale time-series datasets.

Rui Meng, Herbie Lee, Kristofer Bouchard

This paper presents an efficient variational inference framework for deriving a family of structured gaussian process regression network (SGPRN) models. The key idea is to incorporate auxiliary inducing variables in latent functions and jointly treats both the distributions of the inducing variables and hyper-parameters as variational parameters. Then we propose structured variable distributions and marginalize latent variables, which enables the decomposability of a tractable variational lower bound and leads to stochastic optimization. Our inference approach is able to model data in which outputs do not share a common input set with a computational complexity independent of the size of the inputs and outputs and thus easily handle datasets with missing values. We illustrate the performance of our method on synthetic data and real datasets and show that our model generally provides better imputation results on missing data than the state-of-the-art. We also provide a visualization approach for time-varying correlation across outputs in electrocoticography data and those estimates provide insight to understand the neural population dynamics.

Mahesh Balasubramanian, Trevor Ruiz, Brandon Cook et al.

The analysis of scientific data of increasing size and complexity requires statistical machine learning methods that are both interpretable and predictive. Union of Intersections (UoI), a recently developed framework, is a two-step approach that separates model selection and model estimation. A linear regression algorithm based on UoI, $UoI_{LASSO}$, simultaneously achieves low false positives and low false negative feature selection as well as low bias and low variance estimates. Together, these qualities make the results both predictive and interpretable. In this paper, we optimize the $UoI_{LASSO}$ algorithm for single-node execution on NERSC's Cori Knights Landing, a Xeon Phi based supercomputer. We then scale $UoI_{LASSO}$ to execute on cores ranging from 68-278,528 cores on a range of dataset sizes demonstrating the weak and strong scaling of the implementation. We also implement a variant of $UoI_{LASSO}$, $UoI_{VAR}$ for vector autoregressive models, to analyze high dimensional time-series data. We perform single node optimization and multi-node scaling experiments for $UoI_{VAR}$ to demonstrate the effectiveness of the algorithm for weak and strong scaling. Our implementations enable to use estimate the largest VAR model (1000 nodes) we are aware of, and apply it to large neurophysiology data 192 nodes).

Tayo Ajayi, David Mildebrath, Anastasios Kyrillidis et al.

We present theoretical results on the convergence of \emph{non-convex} accelerated gradient descent in matrix factorization models with $\ell_2$-norm loss. The purpose of this work is to study the effects of acceleration in non-convex settings, where provable convergence with acceleration should not be considered a \emph{de facto} property. The technique is applied to matrix sensing problems, for the estimation of a rank $r$ optimal solution $X^\star \in \mathbb{R}^{n \times n}$. Our contributions can be summarized as follows. $i)$ We show that acceleration in factored gradient descent converges at a linear rate; this fact is novel for non-convex matrix factorization settings, under common assumptions. $ii)$ Our proof technique requires the acceleration parameter to be carefully selected, based on the properties of the problem, such as the condition number of $X^\star$ and the condition number of objective function. $iii)$ Currently, our proof leads to the same dependence on the condition number(s) in the contraction parameter, similar to recent results on non-accelerated algorithms. $iv)$ Acceleration is observed in practice, both in synthetic examples and in two real applications: neuronal multi-unit activities recovery from single electrode recordings, and quantum state tomography on quantum computing simulators.